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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

#312. If

verify

.

#313. Show that

.

#314. Two dice are thrown together. What is the probability of getting a total of 8 or a product of 12?

#315. Prove that

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

#316. Prove that

#317.If a line passes through the midpoint of AB where A is (3,0) and B is (5,4) and makes an angle of 60° with tehe x-axis, find its equation.

#318. The angle of elevation of a tower at a point is 45° . After going 20 meters towards the foot of the tower, the angle of elevation of the tower becomes 60° . Claculate the height of the tower.

#319. Find the equation of the straight line joining the point of intersection of

3x - y + 9 = 0 and 2y = x - 4 = 0 to the point of intersection of 2x + y = 4 and

2y = x + 3.

#320.The vertices of a triangle are A(1,8), B(-2,4), and C(8, -5). m and N are the midpoints of AB and AC. Show that MN is parallel to BC and

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

#321. In an Arithmetic progression,

Find the first term and the common difference.

#322. A cylndrical pillar is 3.5 meters in diameter and 20 meters high. Find its volume.

#323. Find the point which divides the line joining the points (-2, 6) and (3, 6) internally in the ratio 3:2.

#324. Prove that the points (9,0), (1,4), and (11,-1) are collinear.

#325. If sin θ = cos θ, where θ is an acute angle, find the value of 2tan² θ - sin² θ - 1.

#326. The mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and also the sum of the squares of all the items.

#327. The sum of the three digits in a three digit number is 24. Twice the tenth digit is equal to the sum of the digits in the other two places. if 198 is added to the number, then the digits would be in the reversed order. Find the number.

#328 : Factorize:-

#329. If

find

.

#330. The mid-points of three sides of a triangle are (5, -3), (-5, 3), and (6, 6). Find the equations of the sides of the traingle.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

331. Find a and b if

is a factor of

.

#332. Find the values of a and b if 9x-2) is a common factor of

#333. If (x-7) and (x-4) are factors of

find the values of p and q.

#334. If (x-1), (x+2), and (x-2) are the factors of

find a, b, and c.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

#335, Two dices contain the numbers from 1 to 6 and 1 to 6. By using these 6 numbers all calendar dates from 01 to 31 must be displayed by rearranging the dices in any way. What are the six numbers each dice contains?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

# 328

By the rational root theorem:

Can only have these rational roots {-1/1,-1/2,-2/2,-2/1,1,1/2,2}

plugging them in we get roots of -2,1/2 and 1

Which means the factorization is of the form

*Last edited by bobbym (2009-10-18 01:51:17)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

Outststading!!!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi ganesh;

*Last edited by bobbym (2009-06-12 20:58:49)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

I shall let you know soon!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 140

Thank you for the interesting and challenging puzzles Ganesh.

*Last edited by Fruityloop (2009-06-18 06:01:04)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

*Last edited by bobbym (2009-06-22 01:19:21)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049

hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

Hi zetafunc,

The solution #321 is correct! Well done!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.

May his adventurous soul rest in peace at heaven.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

Hi Monox D. I-Fly,

The solution #315 is correct! Excellent! Now, I am unable to concentrate on essay type problems! Excuse!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000

Too bad I want to prove all the trigonometry identities problem, though.

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.

May his adventurous soul rest in peace at heaven.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

Hope you understand, Monox D. I-Fly!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

Hi

#321 solution is a=9 and d=6

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

Hi,

The solution #321 is correct. Neat work, 666 bro!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

#329 solution is (x+y) ((1-2q)) /(x-y)

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

The solution of #262 is -(a+nd)

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

The solution of # 314 is (7/36).

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,477

Hi,

I get

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

But I got this is answer in an different way.

Let A and B are two events.

Total number of outcomes=36

A= getting sum of 8

B= getting a product of 12

P(A) = probability of the dices getting sum of 8= (5/36)

P(B) = probability of the dices getting product of 12 = (4/36)

P(A&B) = probability of getting both sum of 8 and product of 12= (2/36)

P(AUB) = probability of getting sum of 8 or getting a product of 12.

so, we should find P(AUB)

Then P(AUB) = P(A) +P(B) -P(A&B)

Now, P(AUB) = (5/36) +(4/36) -(2/36)

= (7/36)

(∴) P(AUB) =(7/36).

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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